# Questions tagged [young-tableaux]

For standard Young tableaux, semistandard Young tableaux, and other related two-dimensional arrays of numbers like plane partitions. Including their combinatorial theory and their application in representation theory and algebraic geometry.

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### A problem about the existence of increasing coloring groups

Got stuck on this one for months. Given a sequence of non decreasing positive integers $a_1, .., a_n$, let there be $a_i$ balls labeled the number i, for each $1 \leq i \leq n$. Suppose there is a k ...
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### Major indices of standard tableaux of shapes obtained from addable cells of a given Young diagram

I have a "very" indirect proof that the following fact is true for every Young diagram $\lambda \vdash n$ and every $r \in \{0,\dotsc,n\}$: d_\lambda = \sum_{a \in \mathrm{...
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### Schur functors = Weyl functors in characteristic zero?

I asked this question on Math Stack Exchange https://math.stackexchange.com/questions/4789924/schur-functors-weyl-functors-in-characteristic-zero, but I got no answers, so I ask the same question here....
1 vote
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### Combinatorics behind certain induction of characters of the Coxeter group of type $B_n$

Let $W_n$ be a Coxeter group of type $B_n$ with $n\geq 1$. Concretely, it is generated by a set of simple reflexions $S = \{s_1,\ldots ,s_n\}$ which satisfy the relations $s_i^2 = 1, s_is_j=s_js_i$ as ...
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### Errata for Fulton's "Young tableaux"

Fulton's Young tableaux is one of the best texts on the subject, one which I often recommend and cite for reference. Unlike Fulton/Lang and Fulton/Harris, it is neither an early-dawn draft nor a ...
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### geometric meaning to pairs of SYT indexing for the basis of cohomology ring of full flag variety

For Grassmannians, the Schubert cells can be indexed by certain Young Tableaux, whose partition determines the dimensions of intersections of the chosen subspace with the standard complete flag. For ...
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### Skewed plane partition with only row fillings reversed

The number of plane partitions in a bounded box is well-studied and dates back to MacMahon, at the start of this paper by Sam Hopkins and Tri Lai, p9, they summarized current results on the ...
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### Orthogonality of irreducible and non-isomorphic representations [closed]

Let V and W be any two subspaces of $(\mathbb{C}^d)^{\otimes n}$ such that there exists two irreducible and non-isomorphic representations $\rho_V: G \to GL(V)$ and $\rho_W: G \to GL(W)$. Does this ...
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### Decomposition of tensors into symmetry classes according to Schur functors

I am mainly looking for references on this subject, as I was unable to find any, at least any that answers what I am looking for to a satisfactory degree. As it is well-known and extremely easy to ...
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1 vote
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### Counting certain kinds of Semistandard Young Tableaux

We have a project in which it is natural to count the number of Young Tableau in which part of the weight has been specified. Does anybody know if this idea already appears in the literature? More ...
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### Robinson-Schensted-Knuth (RSK) under restriction

I am curious about the following result concerning the Robinson-Schensted insertion procedure. I can formulate a proof via the Schützenberger evacuation operator, but I have struggled to find such an ...
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### Counting integer partitions below some Young diagram

Question: Given positive, coprime integers $m<n$, consider the Young diagram $Y$ formed by the lattice points in the Cartesian plane lying below the line from $(0,0)$ to $(m,n)$ and within the ...
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### Bijection between forests and skew SYT + Cyclic sieving

Consider the two-row skew shape $\lambda_n = (2n+1,n)/(1)$. The number of standard Young tableaux of this shape is $\binom{3n}{n}-\binom{3n}{n-2}$ (since one can easily biject this to the set of non-...
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### On a proof involving Young symmetrizers acting on tensor spaces

I hope this is not too elementary for this site, but I already asked something similar on MSE which has not received any attention whatsoever. I am extremely unfamiliar with the algebraic/...
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### Addition theorem for Schur function in multivariable

Working with the following problem Expansion in Schur function of negative binomial exponent I need to find the expansion of $$s_{\lambda}(x_1 + y , x_2 +y, \ldots, x_n +y)$$ in terms of schur ...
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### Yamanouchi ribbon tableaux?

Let $s_{\lambda}$ be a Schur function. The set of all such functions are known to be a linear basis of the algebra of symmetric functions. The Littlewood-Richardson coefficients $c_{\nu\mu}^{\lambda}$ ...
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1 vote
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### Status of conjecture of Conrey and Gonek, combinatorial meaning

I was looking at the OEIS on the number of square Young Tableaux. In it Michael Somos referenced a paper of Conrey and Gonek, High Moment's of the Riemann Zeta-Function. Is there an combinatorial ...
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### A question regarding an analog of Young symmetrizer: the product row and column preserving subgroups without sign representation

Consider a rectangular Young diagram $\lambda$ with $n = pq$ boxes, with $p$ rows and $q$ columns. If $C$ is the column preserving subgroup of $\lambda$ and $R$ is the row preserving subgroup, then we ...
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### Bender-Knuth involutions for symplectic (King) tableaux

First let me recall the combinatorial theory of the characters of $\mathfrak{gl}_m$, a.k.a., Schur polynomials. For a partition $\lambda$, a semistandard Young tableaux of shape $\lambda$ is a filling ...
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### Consequences of Littlewood-Richardson rule

I am trying to read Deligne's paper 'Categories Tensorielles', and in the first chapter Deligne states some results obtained from the Littlewood-Richardson rule that I do not understand. He states: '...
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### Expansion of polytabloids in the standard basis

would like to know the most efficient way to write a polytabloid in terms of standard ones. I know the Garnir elements, but using them to do calculations is hard. I also read about "quadratic ...
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### Refined reverse plane partition generating function

I have a simple question about the generating function for reverse plane partitions: $$\sum_{\pi \in RPP(\lambda)} z^{|\pi|}= \prod_{s \in \lambda} \frac{1}{1-z^{h_{\lambda}(s)}}$$ There's a ...
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### RSK correspondence

Up to now, what are the difference ways we know to define RSK correspondence? I already know: By insertion and recording tableau. Ball construction or Viennot's geometric construction. Growth diagram ...
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### Plane partitions with equal margins

A plane partition of $n$ is an table of integers $A=(a_{ij})$ which add up to $n$ and non-increase in rows and columns. For example, $$A= \begin{matrix} 331 \\ 32 \ \ \\ 11 \ \ \end{matrix}$$ is a ...
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